The symmetry properties of periodic nanostructures determine their interaction with light. Materials that are periodically structured on an optical length scale, known as photonic crystals, can exhibit exotic optical properties, such as lossless reflection, superprism effect, and high-quality-factor (Q) resonance. The optical properties of the photonic crystals are determined by the coupling of the electromagnetic states (i.e., energy, wave vector, and polarization) in the materials to outside radiation. The structural symmetry plays a key role in the selection of the states to be coupled to the external radiation. For example, certain states are forbidden to couple to incident radiation because of the symmetry mismatch between the states and the light. As a consequence of the uncoupling, light absorption and emission are minimal at the frequencies of such uncoupled states. Thus, symmetry control is important in optical and optoelectronic devices that consist of photonic nanostructures.
When the incident light and the electromagnetic eigenstate in the structure have the same symmetry, their interaction is possible. Oppositely, if their symmetry is dissimilar, they are orthogonal to each other and the incident light is reflected. In nanostructured optoelectronic devices, optical absorption or emission is facilitated by resonant coupling between the eigenfield and the propagating light. For example, in solar cells, optical absorption happens strongly at resonance and a number of absorption peaks can arise in the spectrum. In general, the efficiency of the solar cells will increase as the number of absorption peaks in a spectral range increases. These resonant absorption peaks are possible only when the symmetries of the incident light and the eigenmode match each other. Because of this strict symmetry condition for the coupling of the photonic mode to light, many modes cannot be excited in highly symmetric structures. However, when the symmetry of the structures is lowered, the number of resonant peaks increases and hence the device efficiency is enhanced.
Crystalline silicon (c-Si) solar cells utilize c-Si wafers that are typically 100-300 μm thick. Such thick wafers comprise a significant portion of the overall cost of solar modules. The use of thinner c-Si films having a thickness of from about 1 to about 10 μm would be desirable for reducing the cost. However, the optical absorption in such thin c-Si films is much less than that of thick films, and highly efficient light trapping is necessary to achieve the comparable level of efficiency of the thick films.
For crystalline silicon (c-Si) based solar cells, light absorption near the bandgap is relatively weak. Meanwhile, various light-trapping schemes exist today to enhance light absorption. These schemes include light scattering by nanoparticles, random surface corrugation, nanorod arrays, and diffraction gratings. To compensate for their weak absorption, thick c-Si solar cells use light-trapping structures on the order of 10 μm in size, in conjunction with an antireflection (AR) coating, on the front surface of the solar cell facing the sun. This dimension is much larger than the usable wavelengths (300 nm-1.1 μm) of sunlight spectrum, where the wavelength corresponding to the Si bandgap is ˜1.1 μm. In this case, ray tracing based on geometric optics is used to find an optimum structure for light-trapping.
Various factors other than symmetry also need to be considered for optimal optical performance depending on applications. For example, for solar photovoltaics, it is important to trap light inside photoactive layers to enhance energy conversion efficiency. For light-trapping, it is desired that the surface nanostructures on substrates, such as c-Si, be tapered. In this case, the optical density changes gradually and the electromagnetic states in the structures couple well to light. As discussed above, thin films of c-Si are highly desirable to reduce the cost of solar cells. However, the light-trapping structures on the order of 10 μm cannot be used in thin films (˜1-10 μm) whose thickness is comparable to or less than the typical structure dimension. That is, the size of light-trapping structures for thin films must be of submicron dimensions. In this case, the physical mechanism of light-trapping becomes very different from the case of thick films as the structure size becomes comparable to the solar spectrum wavelengths. Nonetheless, incorporation of sub-micron light-trapping features could reduce the c-Si solar cell thickness by two orders of magnitude, while achieving the same efficiency as thick flat c-Si films with an antireflection coating. However, a full utilization of nanostructure symmetry in optical and optoelectronic devices has been limited by the lack of efficient fabrication methods.
What is needed, therefore, are methods to fabricate structures that utilize symmetry breaking in periodic nanostructures that can be used to obtain desired optical properties in nanophotonic devices. Additionally, it is known that a slow variation in locally periodic nanostructures supports adiabatic transformation of optical waves, making such variations an efficient optical transmission medium. A gradual variation in nanostructure symmetry would be equally efficient to achieve the high transmission for optical waves. However, realizing such gradual change in nanostructure symmetry over a macroscopic range has remained a challenge.